An approach to fractal construction in m-metric spaces via F-contractions

Fractals are being used in mathematical modeling, computer graphics and natural science because they have the properties of self-similarity and recursivity. In this paper we have introduced an alternative method on how to establish a certain class of fractals by means of finite family of F-contraction mappings in a complete M-metric space. The new methodology generalizes the classical concept of contraction mappings to allow for broader class of contractive conditions that can be applied, in order to produce a larger category of mappings responsible for the generation of fractals. In this framework a number of new fixed-point theorems for iterated function systems under various contraction assumptions are proved. In order to exemplify the theoretical results, appropriate examples which present the construction of fractals by means of the accomplished results are given. The results of this study extend, unify and generalize several existing ones, they investigate the deep interrelation between fixed point theory and fractal geometry while providing new aspects for many open problems.